Margin
Maximise the margin by minimising ‖w‖.
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11
Supervised learning
Support Vector Machines
Classifiers that maximise the margin, and kernels that bend the boundary.
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What you’ll take away
- SVMs choose the separating hyperplane with the widest margin.
- Only support vectors determine the boundary.
- C trades margin width against training errors (hinge loss).
- Kernels give curved boundaries by working in an implicit feature space.
Major concepts (syllabus)
Maximum-margin classification, support vectors, kernels, nonlinear decision boundaries
Lessons
- Maximum-margin classificationThe separating hyperplane furthest from both classes.9 min
- Support vectorsThe few points that define the boundary.7 min
- Soft margins and hinge lossAllowing violations, controlled by C.9 min
- KernelsInner products in a feature space without computing it.10 min
- Nonlinear decision boundariesRBF and polynomial kernels in action.8 min
Key formulas
Soft-margin SVM
Margin plus hinge penalties.
RBF kernel
Similarity decaying with distance.
Key terms
- Hinge loss
- max(0, 1 − y·f(x)): the SVM loss, zero beyond the margin.
- Kernel trick
- Computing inner products in a high-dimensional feature space directly via a kernel function.
- Margin
- Distance between the decision boundary and the nearest training points.
- RBF kernel
- Gaussian kernel exp(−γ‖x − z‖²): similarity that decays with distance.
- Support vectors
- Training points on or inside the SVM margin that define the boundary.
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